So I want to know if I can reinstall iPhoto without losing my photos?
You photos are in the iphoto Library and not in the iPhoto application, so reinstalling iPhoto will not delete your photos. But the problem seems to be with your iPhoto Library and not with iPhoto.
I've tried hitting the command + option key when starting iPhoto same problem.
How dis you try that? To run the First Aid tools you need to keep holding down the keys when launching iPhoto until you are seeing the First Aid panel. Did you do it this way?
If you tried the First Aid Tools without success, rebuild with iPhoto Library Manager as described by Trence Devlin:
uprgraded to yosemite all good but iphoto crashes every time I attempt to upgrade the photo library
Download iPhoto Library Managerand use its rebuild function. (In early versions of Library Manager it's the File -> Rebuild command. In later versions it's under the Library menu.)
This will create an entirely new library. It will then copy (or try to) your photos and all the associated metadata and versions to this new Library, and arrange it as close as it can to what you had in the damaged Library. It does this based on information it finds in the iPhoto sharing mechanism - but that means that things not shared won't be there, so no slideshows, books or calendars, for instance - but it should get all your events, albums and keywords, faces and places back.
Because this process creates an entirely new library and leaves your old one untouched, it is non-destructive, and if you're not happy with the results you can simply return to your old one.
Download iPhoto Library Manager here: http://www.fatcatsoftware.com/iplm/